5.7a Selected Problem Answers

Question 2

$\theta=\frac{1}{EI} [ 0.333 wLx^2 - 0.167 wx^3- 0.0417 \frac{wx^4}{L} - 0.0611 wL^3 ]$
$\Delta=\frac{1}{EI} [ 0.111 wLx^3 - 0.0417 wx^4- 0.00833 \frac{wx^5}{L} - 0.0611 wxL^3 ]$

Question 3

$\theta =
\begin{cases}
\frac{1}{EI}[Mx-\frac{PLx}{2}+\frac{Px^2}{2}] & \quad \text{if } 0 < x < \frac{L}{2}\\
\frac{1}{EI}[Mx-\frac{PL^2}{8}] & \quad \text{if } \frac{L}{2} < x < L\\
\end{cases}$
$\Delta =
\begin{cases}
\frac{1}{EI}[\frac{Mx^2}{2}-\frac{PLx^2}{4}+\frac{Px^3}{6}] & \quad \text{if } 0 < x < \frac{L}{2}\\
\frac{1}{EI}[\frac{Mx^2}{2}-\frac{PL^2x}{8}+\frac{PL^3}{48}] & \quad \text{if } \frac{L}{2} < x < L\\
\end{cases}$

Question 4

$\theta_{mid} = \ang{2.2}\curvearrowright$, $\Delta_{mid} = \SI{75.8}{mm}\downarrow$, $\theta_{B} = \ang{2.5}\curvearrowright$, $\Delta_{B} = \SI{225}{mm}\downarrow$

Question 5

$\theta_{B,left} = \ang{0.74}\curvearrowright$, $\Delta_{B} = \SI{55.9}{mm}\downarrow$, $\theta_{B,right} = \ang{0.69}\curvearrowleft$, $\Delta_{D} = \SI{30.5}{mm}\downarrow$

Question 6

Local maximum deflection of $\SI{1.66}{mm}\downarrow$ at $x=\SI{1.14}{m}$
[POTENTIAL ERROR: Local maximum deflection of $\SI{10.2}{mm}\uparrow$ at $x=\SI{4.05}{m}$]
Absolute maximum deflection of $\SI{402}{mm}\downarrow$ at $x=\SI{13}{m}$ (end of cantilever)

Question 7

[ERROR: Absolute maximum deflection of $\SI{45.1}{mm}\downarrow$ at $x=\SI{3.53}{m}$]

Question 8

Same answers as question 5.

Question 9

$\theta_{D} = \ang{0.25}\curvearrowleft$, $\Delta_{B} = 0$, $\theta_{B} = \ang{2.0}\curvearrowright$, $\Delta_{D} = \SI{52.2}{mm}\uparrow$

Question 10

$\theta_{C} = \ang{0.12}\curvearrowright$, $\Delta_{C} = \SI{3.59}{mm}\downarrow$, $\theta_{B} = \ang{0.136}\curvearrowright$, $\Delta_{B} = \SI{10.3}{mm}\downarrow$

Question 11

$I \geqslant \SI{132e6}{mm^4}$

Question 12

[ERROR: $I \geqslant \SI{4520e6}{mm^4}$]

Question 13

$\Delta_D = \SI{263}{mm}\downarrow$

Question 14

[ERROR: $\theta_{A} = \ang{0.062}\curvearrowright$, $\Delta_D = \SI{0.231}{mm}\downarrow$]

Question 15

$I \geqslant \SI{430e6}{mm^4}$

Question 16

$I \geqslant \SI{2260e6}{mm^4}$

Question 17

$\Delta_C = \SI{0.557}{mm}\uparrow$

Question 18

$\theta_{A} = \ang{1.70}\curvearrowleft$, $\Delta_A = \SI{120}{mm}\downarrow$

Question 19

$\theta_{D} = \ang{0.769}\curvearrowright$, $\Delta_E = \SI{61.3}{mm}\rightarrow$

Question 20

$\Delta_B = \SI{1.44}{mm}\downarrow$, $\Delta_H = \SI{9.15}{mm}\rightarrow$

Question 21

$\Delta_C = \SI{7.83}{mm}\uparrow$, $\Delta_F = \SI{0.780}{mm}\downarrow$

Question 22

$A \geqslant \SI{227}{mm^2}$

Question 23

[ERROR: $A \geqslant \SI{324}{mm^2}$]

Question 24

$\Delta_F = \SI{2.40}{mm}\rightarrow$

Question 25

$\Delta_B = \SI{2.50}{mm}\uparrow$